Oil and the Dollar
This paper develops a simple theoretical model of the effect of an oil price increase on exchange rates. The model shows that the direction of this effect depends on a comparison of the direct balance of payments burden of the higher oil price with the indirect balance of payments benefits of OPEC spending and investment. In the short run, what matters is whether the U.S. share of world oil imports is more or less than its share of OPEC asset holdings; in the long run, whether its share of oil imports is more or less than its share of OPEC imports. Casual empiricism suggests that the initial effect and the long run effect will run in opposite directions: an oil price increase will initially lead to dollar appreciation, but eventually leads to dollar depreciation.
Krugman, Paul. "Oil and the Dollar." Economic Interdependence Under Flexible Exchange Rates, edited by J. Bhandari and B. Putnam, pp. 179-190. Cambridge: Massachusetts Institute of Technology, 1983.